Pure Gaussian States in Open Quantum Systems

Pure Gaussian states are of great practical importance in continuous-variable quantum information processing. Therefore, preparation of pure Gaussian states is an important task. This thesis considers the preparation of pure Gaussian states using linear open quantum systems. By appropriately designing coherent and dissipative processes, an open quantum system can be made strictly stable and will evolve into a target pure Gaussian state.First, we show that any pure Gaussian state can be generated by constructing a cascaded quantum system. This cascaded quantum system is a series connection of several subsystems in which the output of one is fed as the input to the next. Second, we consider a system of quantum harmonic oscillators that have no Hamiltonian coupling but are coupled by virtue of their collective coupling to a single common reservoir. We give a complete parametrization of all pure Gaussian states that can be generated by this type of system. Third, we consider a system of quantum harmonic oscillators with beam-splitter-like Hamiltonian interactions and with a single local dissipative process. We give a complete parametrization of all pure Gaussian states that can be generated by this type of system. Fourth, we consider a quantum harmonic oscillator chain with nearest-neighbour beam-splitter-like Hamiltonian interactions and with a single reservoir which acts locally on the central oscillator. We give a complete parametrization of all pure Gaussian states that can be generated by this type of chain.These parametrizations allow us to calculate the covariance matrices of pure Gaussian states and then determine their entanglement properties. Entanglement is a crucial resource behind the advantages offered by quantum technologies